5690:6600(56·88):88

To solve the expression \( 5690:6600(56.88):88 \), we will break it down step by step.

1. Start with the first part: \( 5690:6600 \).

   • This can be interpreted as a fraction: \( \frac{5690}{6600} \).

2. Calculate \( \frac{5690}{6600} \).

   • Dividing both the numerator and the denominator by their greatest common divisor (gcd), which is 10 in this case, we get: \[ \frac{569}{660} \]
   • In decimal form: \[ 569 \div 660 \approx 0.8636 \]

3. Next, take the value obtained and multiply it by \( 56.88 \): \[ 0.8636 \times 56.88 \approx 49.113 \]

4. Finally, divide the result by \( 88 \): \[ \frac{49.113}{88} \approx 0.558 \]

The final answer is approximately \( 0.558 \).